Question

In the figure, AB//DC, angle DPB=70° and arc BC=2 cm.
(a) Find BCD and BOD.
(b) Hence find BAD and ADC
(c) Find the length of arc AD.

Answer 1

is it a circle?

Answer 2

of course..

Answer 3

for it is an inscribed quadrilateral, DPB+DAB=ABP+ADP=180
Therefore DAB=180-70=110
also as an inscribed quadrilateral BOD=2BPD=140
DBC=90
so DO=BO=OC, soDOB=2DCB=2OBC

Answer 4

so BCD=70

Answer 5

@Frank_Shank I am sorry that the question cannot use cyclic quad. theorem.
Besides, I forgot to tell you that I have problem in part c only...

Answer 6

you got the BOC(180-140=40) perimeter=2cm*360/40=18 so r=9/pi
and DAO=ADC=70 DOA=40
AO=DO=9/pi
it's easy to get the length of AD now

Answer 7

DOC is not a diameter...

Answer 8

you sure………………？？

Answer 9

yes, the book draw something like this,

Answer 10

anyway do you know AOD and BOC?

Answer 11

no

Answer 12

similar triangles?